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0, 0, 0, 2, 2, 4, 4, 7, 9, 11, 11, 14, 14, 16, 18, 22, 22, 25, 25, 28, 30, 32, 32, 36, 38, 40, 43, 46, 46, 49, 49, 54, 56, 58, 60, 64, 64, 66, 68, 72, 72, 75, 75, 78, 81, 83, 83, 88, 90, 93, 95, 98, 98, 102, 104, 108, 110, 112, 112, 116, 116, 118, 121, 127, 129, 132, 132
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Excess of prime-power exponents in n!.
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FORMULA
| a(n) = A046660(n!) = A046660(A000142(n)) = A022559(n) - A001221(n!) = A001222(n!) - A000720(n).
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EXAMPLE
| n=46: prime powers in factorization of 46! are {42,21,10,6,4,3,2,2,2,1,1,1,1,1}. Sum of the exponents is 97. It has 14 distinct prime divisors, so a(46)=97-14=83.
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CROSSREFS
| Cf. A046660, A000142, A022559, A001221, A001222, A000720, A144494.
Sequence in context: A005308 A151532 A056503 * A143419 A183566 A034396
Adjacent sequences: A055633 A055634 A055635 * A055637 A055638 A055639
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jun 07 2000
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EXTENSIONS
| Simpler definition from Alan Worley (aw(AT)xiboo.co.uk), Dec 10 2008
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